Elevation Grade Calculator

What the elevation grade calculator does

Grade is how steep a slope is, the kind of figure that turns up on a driveway, a drainage run, a ramp, or a stretch of road. This works it out and lets you solve it from either direction. Give it a rise and a run and it returns the grade; give it the grade and one measurement and it fills in the other.

It hands you the slope as a percent, a ratio, and an angle, since different jobs ask for different forms. Below is how it works and what a given grade actually means on the ground.

How to use it

1. Pick what you want to find. Grade from a rise and run, or solve for the Vertical Change or the Horizontal Change when you already know the grade.
2. Enter the two values it asks for, each with its unit. The rise and run can be in different units.
3. Press Calculate for the result, or Reset to clear it.

How grade is worked out

Grade is simply how much something rises compared with how far it travels horizontally:

Grade = rise ÷ run

Multiply that by 100 and you have the percent grade, the most common form. Take the arctangent of it and you have the slope as an angle in degrees. When you give the calculator a grade instead and ask for the rise or the run, it just rearranges the same relationship, multiplying or dividing to find the missing side.

Percent, ratio, and degrees

The result shows the slope a few ways because each trade leans on a different one. The percent is what roads, driveways, and drainage plans use, a 5 percent grade rising 5 units for every 100 it runs. The ratio and decimal are the plain rise over run. The degrees figure is the actual angle, handy when you are thinking about it geometrically.

One catch to keep in mind: percent and degrees are not interchangeable. A 100 percent grade is a 45 degree slope, not 90, because at 45 degrees the rise finally equals the run. Percent can climb past 100, but the angle never reaches 90 until the slope is vertical.

A worked example: 3 ft over 50 ft

Say the ground rises 3 feet over a horizontal run of 50 feet.

The grade is 3 ÷ 50 = 0.06, which is a 6 percent grade. As an angle that is the arctangent of 0.06, about 3.4 degrees.

Six percent sounds gentle, and as an angle it barely is, but on a road that is a noticeable hill, which is the point of the next section.

What counts as a steep grade

A percent on its own does not tell you much until you have a feel for the range. For drainage, you usually want at least a gentle fall of around 2 percent away from a building so water runs off rather than pooling. Roads are built fairly flat, with main highway grades generally kept to around 6 percent, which is why a 6 percent stretch gets a warning sign. Driveways can go steeper, but much past 15 percent and you risk scraping and icing trouble.

Ramps for accessibility are the strictest of all: the standard limit is a 1 in 12 slope, which is about 8.3 percent, and going steeper makes a ramp hard or unsafe to use. So the same calculator covers everything from a barely-there drainage fall to a slope that needs handling with care.

Questions people ask

What is a percent grade?

It is the rise divided by the run, times 100. A slope that climbs 6 feet over 100 feet of run is a 6 percent grade.

How do I convert grade to degrees?

Take the arctangent of the grade as a decimal. A 6 percent grade, or 0.06, works out to about 3.4 degrees. The calculator shows both.

What is the maximum grade for a driveway?

Gentler is easier to live with, and much beyond about 15 percent you start risking scraping and icing. Local rules vary, so check before building a steep one.

What slope do I need for drainage?

A fall of around 2 percent away from a building is a common target, enough for water to run off without pooling.

References

A quick note on the numbers. Grade is plain arithmetic, the rise over the run as a ratio, a percent, or an angle through the arctangent. The accessible ramp limit of 1 in 12 comes from the US Access Board's accessibility guidelines. The unit conversions follow the US National Institute of Standards and Technology guide.

1. US Access Board, accessibility guidelines for ramps and running slope. https://www.access-board.gov
2. National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811